Geodesic
On topological algebras of analytic functionals with a multiplication defined by translations
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 14-22

Voir la notice de l'article provenant de la source Math-Net.Ru

We define a multiplication — convolution in the dual of a countable inductive limit $E$ of weighted Fréchet spaces of entire functions of several variables. This algebra is isomorphic to the commutant of the system of partial derivatives in the algebra of all continuous linear operators in $E$. In the constructed algebra of analytic functionals in two pure cases a topology is defined. With this topology the mentioned algebra is topological and it is now topologically isomorphic to the considered commutant with its natural operator topology. It is proved that in this pure situations the present algebra has no zero divisors provided that polynomials are dense in $E$. We show that this condition is essential for the validity of the last statement.
Keywords: weighted space of entire functions, algebra of analytic functionals, topological algebra, convolution operator.
Mots-clés : communant 
@article{VSGU_2018_24_3_a1,
     author = {O. A. Ivanova and S. N. Melikhov},
     title = {On topological algebras of analytic functionals with a multiplication defined by translations},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {14--22},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a1/}
}
TY  - JOUR
AU  - O. A. Ivanova
AU  - S. N. Melikhov
TI  - On topological algebras of analytic functionals with a multiplication defined by translations
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2018
SP  - 14
EP  - 22
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a1/
LA  - ru
ID  - VSGU_2018_24_3_a1
ER  - 
%0 Journal Article
%A O. A. Ivanova
%A S. N. Melikhov
%T On topological algebras of analytic functionals with a multiplication defined by translations
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2018
%P 14-22
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a1/
%G ru
%F VSGU_2018_24_3_a1
O. A. Ivanova; S. N. Melikhov. On topological algebras of analytic functionals with a multiplication defined by translations. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 14-22. http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a1/